The present invention relates to a Fresnel-type lens for use in integrated optical structures.
For many years, remote data transmission methods have used transmission by light waves on the basis of light guides which are usually constituted by ultra-fine optical fibres or optical waveguides incorporating a pile of sandwiches formed by alternating layers of transparent materials, which are generally also semiconductive. Thus, the simplest transparent waveguide is a sandwich constituted by a material having a high refractive index inserted between two materials having lower refractive indices. In such a waveguide a light beam is propagated in a zig-zag path in the median layer, whilst undergoing total reflections alternately on one and then on the other of the interfaces. The possibility of producing light sources in the form of a semiconductor diode laser and of obtaining the modulation of the transported light beam by modification of the refractive index of a semiconductor layer by means of applied external electric fields makes it possible to produce a complete circuit for the emission, transmission and decoding of information in light form by methods well known in the construction of integrated semiconductors. It is for this reason that this novel remote data transmission optics is called "integrated optics".
An extremely simple known waveguide construction is shown in FIG. 1. It comprises a substrate 1 of index n.sub.s covered by a guidance layer 2 of index n.sub.g. The surrounding air of index n=1 serves as the second substrate. In such a waveguide, propagation is assumed to take place in the axis Oz perpendicular to the drawing. The solving of the Maxwell equations shows that there are two possible propagation modes, each corresponding to a particular polarization of the light. In the so-called transverse electrical mode (TE) the electrical field E is parallel to the direction Oy, whilst in the so-called transverse magnetic mode (TM) the magnetic field H is parallel to the direction Oy. Each of these modes is characterized by its effective propagation in dex n.sub.eff, linked with the propagation or transmission speed v of the light wave using formula ##EQU1## in which c is the speed of light in vacuo. The value of n.sub.eff is itself dependent on the value of the different indices of the layers of the system constituting the waveguide and on their relative thicknesses. Thus, in integrated optics, the speed of a light wave can be modified either by varying the optical index or by varying the thickness of the different layers present. This observation is of fundamental importance and will be used, as will be shown hereinafter, within the scope of the present invention.
Finally, it is useful to recall that the light waves propagating in an optical guide is sometimes evanescent, at least in the two extreme media, i.e. in the substrates. This means that it is not completely contained within the guidance layer, but in a nonhomogeneous manner penetrates immediately adjacent layers by a very limited thickness. In the special case of the waveguide of FIG. 1, the necessary and sufficient condition to obtain the presence of an evanescent wave in the extreme media constituted by substrate 1 and the surrounding air is provided by the following relationship between the different indices of the constituent layers and the effective index:
1&lt;n.sub.s &lt;n.sub.eff &lt;n.sub.g.
By transposing phenomena known in the conventional optics, attempts have been made to provide in the form of integrated components structures equivalent to the previously known structures in order to ensure the correct propagation of light in a space having only two dimensions instead of the usual three dimensions of conventional optics. Thus, for transforming a plane light wave into a spherical wave, i.e. making a parallel light beam converge at a point called the focus, in conventional optics systems of lenses are used which, to a greater or lesser extent, have optical defects known as aberrations and which lead to inadequacies with regard to the concentration quality of the light at the focus. In order to obviate this disadvantage, the physisist Fresnel developed in conventional optics lenses which are known by his name and which make it possible, by correcting the aberrations due to the two convergent edges of the lenses to obtain an almost perfect concentration of the light at their focus.
With reference to FIG. 2, we will firstly describe the known operating principle of a Fresnel lens in conventional optics. Thus, with reference to FIG. 2, we will consider a plane light wave (.SIGMA.) arriving in zone I in the left-hand part of the drawing on a diffracting wave plane E. On the basis of the Fresnel Huyghens principle, each of the points of screen E can be considered as light source, whose vibrations are of form: ##EQU2## If it is accepted that all the points of screen E are in phase and if this screen is taken as the original of the phases.
It is also possible to take a thin diffractive circular band, like 3 in FIG. 2, and locate it between the two circumferences passing through points P and P' and at distance R from axis O and dr from one another. It is possible to write that the vibration diffracted at a point F of the axis of the system, by the circular band 3 of width dr is, to within a coefficient, of form: ##EQU3## in which T is the light vibration cycle, .lambda. its wave length, t the time and x the distance between point P and point F. Under these conditions, to obtain the exact expression of the total vibration diffracted by screen E and at point F it is necessary to form the integral of the above expression from O to r, whilst taking account of the fact that: ##EQU4##
In practical terms, Fresnel worked out a more simple method for calculating this integral which consists of breaking down the surface of screen E located around point O into a certain number of elementary annular bands of centre O such that on passing from the band of order m of radius r.sub.m to the band of order m+1 of radius r.sub.m+1 the distance to point F increases progressively by a half wave length, i.e. .lambda./2. It is then possible to write the following equations: ##EQU5## and EQU X.sub.m.sup.2 =r.sub.m.sup.2 +f.sup.2.
In these formulas, x.sub.m is the distance between point P.sub.m spaced by r.sub.m from point O and point F and .lambda. is the light wave length used. By comparing the two above equations, it is possible to write by replacing in the second x.sub.m.sup.2 by its value taken from the first: ##EQU6##
On ignoring the term in .lambda.2/4, which is justified in practice because the wave length .lambda. is always well below F we then obtain r.sub.m =.sqroot.mf.lambda..
In other words, in order that the initially imposed condition on the variations in the path of the different vibrations diffracted at E by each of the successive annular bands is repeated, the bands must have radii r.sub.m which intercept like the square root of successive integers.
However, on the basis of the very definition the different circular bands of radii r.sub.m have been selected in such a way that on passing from one to the other, the vibration diffracted at F by one zone is phase-displaced by .pi. relative to the preceding, zone, because its path differs by a half wavelength. Therefore, all the annular bands of even rank (m=0, 2, 4, 6 . . . ) firstly diffract at F vibration components in phase with one another, whilst all the bands of uneven rank (m=1, 3, 5 . . . ) diffract at F vibration components in phase with one another and the two groups of vibration components are phase-displaced by .pi. relative to one another.
Under these conditions, if it is wished that the system is really a lens which rigorously makes the parallel beams of wave (.SIGMA.) of zone I converge in phase at point F of zone II in accordance with the spherical wave (.SIGMA.') there are two possible solutions:
The first consists of introducing a phase displacement complementary of .pi. on all the vibration components of the circular bands of the even rank or uneven rank, thus leading to a so-called phase-displaced Fresnel lens.
The second consists of absorbing the light energy of every other band and only leaving even or uneven bands which, as has been seen, are all in phase. This leads to a so-called absorption Fresnel lens having the disadvantage that the amplitude of the light at point F is divided by 2 and consequently its intensity by 4.
In order to produce a Fresnel lens in integrated optics, it is possible to transpose the teachings in connection with conventional optics in the case where light is propagated in a bidimensional media. Experience has shown that the approximation resulting from the fact that the existence of a propagation in accordance with guided modes is neglected is acceptable.
FIG. 3 and FIG. 4, which is a section of FIG. 3 in accordance with one of the overlayers thereof provide a better understanding of the composition of such an integrated Fresnel lens.
This lens also has layers 1 and 2 of the waveguide of FIG. 1 and arrows F.sub.1 indicate the light paths of the plane wave (.SIGMA.) reaching the lens, which is to be transformed into a circular wave (.SIGMA.'), whose beams F.sub.1 ' converge at a point of the axis F constituting the focus of the lens. By comparison with conventional Fresnel lenses, a Fresnel lenses in integrated optics is constituted by a certain number of linear zones parallel to the axis and located at distances rm from the axis such that: ##EQU7##
In the formula, .lambda..sub.o is the wavelength in vacuo of the light radiation used. These linear zones ensure either an appropriate phase displacement of half the incident light or a total absorption of half the light rays so as to only permit the passage in the direction of focus F of vibrations which are in phase producing constructional interferences at said point. In practical terms, the various above zones are provided by overlayers 4 constituted by flat films of length L, thickness W' and index n', as has been seen in FIGS. 3 and 4.
Thus, on superimposing over a length L a layer of index n' and thickness W' as indicated in FIG. 4 on the initial structure of FIG. 1 the value of the effective index for the propagation of a wave in accordance with the guided mode TE is changed, whereby n.sub.eff in zone 5 becomes n.sub.eff ' in zone 6. A guided wave propagated in accordance with the mode TE over a length L in said novel structure consequently acquires a phase displacement ##EQU8## in which .DELTA.n=n.sub.eff '=n.sub.eff. Compared with the phase which it had in the initial structure. Thus, by means of overlayers of this type, it is possible to locally modify the phase displacement of a guided wave by changing the multilayer guiding structure, thus obtaining a phase-displaced Fresnel lens.
Such phase-displaced Fresnel lenses in integrated optical form have already been proposed, cf the article "Fresnel lens in a thin-film waveguide" published in Applied Physical Letters 33(6) on 15.9.1978. This article describes an optical phase-displaced Fresnel lens obtained by means of a certain number of overlayers in the form of flat films, the structure being comparable to that shown in FIGS. 3 and 4. More specifically and as shown in FIG. 5a, the substrate is made from a glass of index n.sub.1 =1.51 and the guidance layer is made from barium oxide BaO of index n.sub.2 =1.55, whilst the plates constituting the various overlayers are made from cerium oxides CeO of index n.sub.3 =2.0. Thus, in this construction, the overlayers are formed from a material whose refractive index exceeds that of the wave guide. This has numerous disadvantages, which can be summarized in the following manner:
(a) the light wave, which is homogeneous in the BaO wave guide is also homogeneous in the CeO overlayer of a higher index. Thus, in this case, the effective index of the guided mode increases continuously with the thickness W of the CeO overlayer, necessitating an excellent control of said thickness W.
(b) The different indices introduced by the layer having a higher index than the guide are also very important. In order to introduce a phase displacement of .pi., the length L of the engraved motif must be very short leading to low precision with regard to the phase displacement introduced ##EQU9## because .DELTA.L is substantially constant and is imposed by technology.
As an example, FIG. 5 shows the real variation curves for .DELTA.n.sub.eff for the mode TE as a function of the thickness W of the CeO overlayer in this case. In the selected working zone (W.about.1000 A) the slope .DELTA.n.sub.eff /dW is approximately 2.10.sup.-4 /A (it should be noted that it is difficult to homogeneously produce layers thinner than 500 A). With a zone length L of 500 um, this corresponds to a variation of the phase displacement .DELTA..phi. of 0.033.pi./A. This means that the control of the thickness W must be better than 10 A which is very difficult of even impossible to carry out in the case of mass production. In addition, hitherto, no absorption-type Fresnel lenses have been produced in integrated optics.